# Optimal Transport for Domain Adaptation through Gaussian Mixture Models

arXiv: https://arxiv.org/abs/2403.13847 · HTML: https://mlsanity.com/paper/2403.13847/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 53 references that are in the map.
- First posted on arXiv 18 Mar 2024.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Deep Visual Domain Adaptation: A Survey](https://mlsanity.com/paper/1802.03601/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [VisDA: The Visual Domain Adaptation Challenge](https://mlsanity.com/paper/1710.06924/) (2017)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [A survey on domain adaptation theory: learning bounds and theoretical guarantees](https://mlsanity.com/paper/2004.11829/) (2020)
- [Theoretical Analysis of Domain Adaptation with Optimal Transport](https://mlsanity.com/paper/1610.04420/) (2016)
- [A Wasserstein-type distance in the space of Gaussian Mixture Models](https://mlsanity.com/paper/1907.05254/) (2019)
- [Optimal Transport for Multi-source Domain Adaptation under Target Shift](https://mlsanity.com/paper/1803.04899/) (2018)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections](https://mlsanity.com/paper/2107.01718/) (2021)
- [Domain Adaptive Neural Networks for Object Recognition](https://mlsanity.com/paper/1409.6041/) (2014)
- [Optimal transport for Gaussian mixture models](https://mlsanity.com/paper/1710.07876/) (2017)
- [Concentration bounds for linear Monge mapping estimation and optimal transport domain adaptation](https://mlsanity.com/paper/1905.10155/) (2019)
- [Multi-Source Domain Adaptation through Dataset Dictionary Learning in Wasserstein Space](https://mlsanity.com/paper/2307.14953/) (2023)
- [Hierarchical Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2112.02073/) (2021)
- [InfoOT: Information Maximizing Optimal Transport](https://mlsanity.com/paper/2210.03164/) (2022)
- [Benchmarking Domain Adaptation for Chemical Processes on the Tennessee Eastman Process](https://mlsanity.com/paper/2308.11247/) (2023)
- [Learning representations that are closed-form Monge mapping optimal with application to domain adaptation](https://mlsanity.com/paper/2305.07500/) (2023)

## Built on by (most cited first, 3 of 3)

- [Lighter, Better, Faster Multi-Source Domain Adaptation with Gaussian Mixture Models and Optimal Transport](https://mlsanity.com/paper/2404.10261/) (2024)
- [SNAP: Low-Latency Test-Time Adaptation with Sparse Updates](https://mlsanity.com/paper/2511.15276/) (2025)
- [A Biconvex Formulation for Stable Transport of Mixture Models with a Unique Solution](https://mlsanity.com/paper/2606.02515/) (2026)

## Abstract (arXiv)

Machine learning systems operate under the assumption that training and test data are sampled from a fixed probability distribution. However, this assumptions is rarely verified in practice, as the conditions upon which data was acquired are likely to change. In this context, the adaptation of the unsupervised domain requires minimal access to the data of the new conditions for learning models robust to changes in the data distribution. Optimal transport is a theoretically grounded tool for analyzing changes in distribution, especially as it allows the mapping between domains. However, these methods are usually computationally expensive as their complexity scales cubically with the number of samples. In this work, we explore optimal transport between Gaussian Mixture Models (GMMs), which is conveniently written in terms of the components of source and target GMMs. We experiment with 9 benchmarks, with a total of 85 adaptation tasks, showing that our methods are more efficient than previous shallow domain adaptation methods, and they scale well with number of samples n and dimensions d.